The first term corresponds to \(\Delta L=0\) , operative in \(D^* \rightarrow D \pi \)  [1]}, the second to \(\Delta L=1\) , for \(Y\)  and \(D_1\)  pionic decay, dots indicate terms with \(\Delta L>1\) .
Using charge conjugation symmetry, restricting to the \(\Delta L=1\)  term and specializing to the \(\pi ^0\)  case, we obtain the hamitonian
\(H^\pi _I=\frac{g}{f_\pi }\frac{q^2}{4m_u}\, i\omega \, \chi ^\dag [ {\mathbf {\xi \cdot }}({\mathbf {\sigma }}_{ u}-{\mathbf {\sigma }}_{\bar{u}}) - (u \rightarrow d)]\chi \, \frac{\pi ^0}{\sqrt{2}} \) 
